In spite of difficulties existing in the measurement of the heat capacity of LM, it was measured with a good precision for liquid Na at normal atmospheric pressure — the recommendations from different sources differ for <1% in the temperature range from normal melting point up to normal boiling

point at normal atmospheric pressure.7,10,67 Higher uncertainty is observed at higher pressures and tem­peratures and on the saturation line.68 The heat capacity of liquid Pb was satisfactorily measured only at temperatures up to about 1400 K5,2 , 8 and with a precision ~5%. At higher temperatures, the available experimental data often give contradictory results. The heat capacity values for liquid Pb in a large range of temperatures at normal atmospheric pressure were estimated by Gurvich and Veyts69 with theoretical models benchmarked on the existing experimental results. Available data on the heat capacity of Pb-Bi(e) are very limited.70-72 In order to describe the temperature dependence of LM heat capacity, often the following correlation is used:

СДГ, p0) = + bcfT + ccf T2 + dcf T -2 [12]

The recommended coefficients of correlation [12] for liquid Na were taken from the compilation of IAEA,26 for Pb from Gurvich and Veyts,69 and for Pb-Bi(e), they were deduced in Sobolev34 on the basis of a review of the existing data and recommen­dations; the coefficients are given in Table 10. The uncertainty is about ±1% forNa and ±(5-7)% forPb and Pb-Bi(e) at temperatures up to T = 1100-1400 K; the uncertainty increases at higher temperatures where no experimental data were found for Pb and Pb-Be(e) in the literature.

The calculated with correlation [10] isobaric heat capacities of liquid Na, Pb, and Pb-Bi(e) are pre­sented in Figure 9 versus temperature.

The isochoric heat capacity can be estimated using correlations for the isobaric heat capacity (cp),

the isothermal compressibility (br), the density (p), and the isobaric volumetric CTE (a^):

pbr

The molar enthalpy (H) of LM as a function of temperature at the given pressure can be presented as a sum of the LM enthalpy at the melting point H(Tm, p) and the LM enthalpy increment caused by temperature increase AH(T — TM, p), which is expressed through an integral of the isobaric heat capacity over temperature:

H (T, p) = H ( Tm, p) + AH (T — Tm, p)

T

= H (Tm, p)-

2.14.4.1 Equation of State

During the past years, considerable progress has been achieved in the development of empirical, semi­empirical, and mechanistic EOS for fluids. Simple thermal EOS is frequently used in engineering practice, which relates the main TD variables pressure, temperature, and volume (or density): F(p, T, p) = 0, which is equivalent to p = p(T, p) considered in Section 2.14.4.1. Knowledge of the temperature and pressure dependence of one of the thermodynamic potentials (e. g., enthalpy H) allows to construct the caloric EOS: H = H(T, p).

The first term on the right-hand side is described by eqn [5] in Section 2.14.4.1. The effect of pressure can be estimated using the information on the sound velocity, thermal expansion, and heat capacity, with the following thermodynamic relationship:

dp _ / 1 MaTa2(T)

dp T ~ U(T)+ cp (t)

The results of the calculation of the pressure coeffi­cient [16] for liquid Na, Pb, and Pb-Bi(e) show34 that it is rather small: the density correction does not exceed 0.04% per 1 MPa of pressure for Na and 0.01% per 1 MPa for Pb and Pb-Bi(e) in the tem­perature range of the normal operation of these cool­ants in Gen IV reactors. Thus, at normal operation pressures of these reactors (0.1—2.0 MPa), the thermal EOS developed at normal atmospheric pressure can be used for design estimations.